Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Forgot your password?
• Apply for membership

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 24th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItextried to bring the old neglected entry [[sSet-category]] roughly into some kind of stubby shape. Added Porter-Cordier and LurieA.3 as references. The former was my motivation for doing this. Eventually it would be good to have here a detailed discussion of $sSet$-category models for $(\infty,1)$-category theory. See the discussion with Tim over in the other thread on the $(\infty,1)$-Yoneda lemma. (I don't have time for this now. I am saying all this in the hope that somebody else has.)

   tried to bring the old neglected entry sSet-category roughly into some kind of stubby shape. Added Porter-Cordier and LurieA.3 as references. The former was my motivation for doing this. Eventually it would be good to have here a detailed discussion of $sSet$-category models for $(\infty,1)$-category theory. See the discussion with Tim over in the other thread on the $(\infty,1)$-Yoneda lemma.

   (I don’t have time for this now. I am saying all this in the hope that somebody else has.)

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeNov 24th 2010
   • PermaLink
   Author: zskoda
   Format: TextThe first line of the entry says simplicial enriched category, while all occurences later seem to say simplicially enriched category. I suppose the latter variant is the usual one. Is the usage of both variants intentional ?

   The first line of the entry says simplicial enriched category, while all occurences later seem to say simplicially enriched category. I suppose the latter variant is the usual one. Is the usage of both variants intentional ?
3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeNov 24th 2010
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexIt now says 'simplicially'! thanks.

   It now says ’simplicially’! thanks.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 24th 2010
   • (edited Nov 24th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded reference to Batanin's article that shows that the homotopy coherent hom-objects between simplicial categories are in fact $sSet-A_\infty$-categories.

   added reference to Batanin’s article that shows that the homotopy coherent hom-objects between simplicial categories are in fact $sSet-A_\infty$-categories.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 30th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded too [[sSet-category]] a (very) brief paragraph on simplicial localization and added the two original references by Dwyer and Kan.

   added too sSet-category a (very) brief paragraph on simplicial localization and added the two original references by Dwyer and Kan.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeNov 30th 2010
   • (edited Nov 30th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded also a remark on how $sSet$-categories serve as a context for modeling $(\infty,1)$-topos theory and included the reference to Toën-Vezzosi's work on this.

   added also a remark on how $sSet$-categories serve as a context for modeling $(\infty,1)$-topos theory and included the reference to Toën-Vezzosi’s work on this.